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the society of his friends said (referring to the newly published
papers of Cauchy), "This is a new mathematic'V
Riemann spent two years at the University of Berlin. During
the political upheaval of 1848 he served with the loyal student
corps and had one weary spell of sixteen hours' guard duty
protecting the jittery if sacred person of the king in the royal
palace. In 1849 he returned to Gottingen to complete his mathe-
matical training for the doctorate. His interests were unusually
broad for the pure mathematician he is commonly rated to be,
and in fact he devoted as much of his time to physical science
as he did to mathematics.
From this distance it seems as though Riemann1 s real interest
was in mathematical physics, and it is quite possible that had
he been granted twenty or thirty more years of life he would
have become the Newton or Einstein of the nineteenth century.
His physical ideas were bold in the extreme for his time. Not
till Einstein realized Riemann's dream of a geometrized (macro-
scopic) physics did the physics which Riemann foreshadowed -
somewhat obscurely, it may be - appear reasonable to physi-
cists. In this direction his only understanding follower till our
own century was the English mathematician William Eongdon
Clifford (1845-79), who also died long before his time.
During his last three semesters at Gottingen Riemann
attended lectures on philosophy and followed the course of
Wilhelm Weber in experimental physics with the greatest
interest. The philosophical and psychological fragments left by
Riemann at his death show that as a philosophical thinker he
was as original as he was in mathematics and science. Weber
recognized Riemann's scientific genius and became his warm
friend and helpful counsellor. To a far higher degree than the
majority of great mathematicians who have written on phy-
sical science, Riemann had a feeling for what is important - or
likely to be so - in physics, and this feeling is no doubt due to
his work in the laboratory and his contact with men who were
primarily physicists and not mathematicians. The contribu-
tions of even great pure mathematicians to physical science
have usually been characterized by a singular irrelevance so
far as the universe observed by scientists is concerned. Riemann,